How this instrument works
A decimal already is a fraction; it just hides the denominator inside its place value. Write 0.75 as "75 hundredths" and you have 75⁄100 without doing any conversion at all — the digits after the point are literally counting parts of a power of ten. This calculator makes that hidden denominator explicit, then simplifies the result the way any fraction gets simplified.
The mechanism is two separate moves. First, scaling: multiplying the decimal by exactly 1,000,000 shifts its point six places right and produces a whole number, Scaled numerator (× 1,000,000) — no rounding is needed as long as the decimal has six or fewer digits after the point. Second, reducing: that scaled number and 1,000,000 are divided by their greatest common divisor, the same Euclidean-algorithm step used to simplify any fraction whatsoever, decimal-born or not.
The fixed scale is also the method's limit. A decimal typed with more than six digits after the point gets rounded to the nearest millionth before reduction begins, and a repeating decimal such as one-third's 0.333… can never land on an exact fraction this way, because no denominator that is a power of ten produces a repeating expansion — only denominators built from prime factors other than 2 and 5 do that, and 1,000,000 is built from nothing but 2s and 5s.
- Type the decimal you want converted into the Decimal field — six digits after the point are captured exactly.
- Scaled numerator (× 1,000,000) shows that decimal shifted six places right into a whole number, before any simplifying happens.
- GCD used to reduce reports the greatest common divisor shared by that scaled number and 1,000,000 — the factor both sides get divided by.
- Read Numerator and Denominator for the finished fraction, already reduced to lowest terms.
Worked example — reducing 0.75 to three quarters
Type 0.75 into Decimal. Scaled numerator (× 1,000,000) reads 750,000, since shifting 0.75's decimal point six places right lands on that whole number exactly, with nothing to round away. GCD used to reduce reports 250,000 — the largest number dividing both 750,000 and 1,000,000 evenly. Divide each by that: 750,000 ÷ 250,000 = 3 and 1,000,000 ÷ 250,000 = 4, so Numerator and Denominator settle on 3 and 4 — the familiar three-quarters, produced by arithmetic rather than recalled from memory.
Check it by reversing the arithmetic: 3 ÷ 4 returns exactly 0.75, confirming nothing was lost in the reduction. The 250,000 is no accident — 750,000 and 1,000,000 share every factor of two and five between them, right down to the last one, because both numbers were built from the same powers of ten in the first place.
Questions
How does this calculator turn a decimal into a fraction?
It scales the decimal into a whole number by multiplying by 1,000,000, then reduces that number over 1,000,000 by dividing both by their greatest common divisor. The first step exposes the fraction that was always hiding in the decimal's place value; the second step just simplifies it, the same as simplifying any other fraction.
Why scale by exactly 1,000,000 instead of counting the decimal places by hand?
A fixed scale means the calculator never has to detect how many digits you typed — it always shifts six places, which covers any decimal with up to six digits after the point. The traditional by-hand method multiplies by 10 raised to however many places are present; scaling by a fixed million sidesteps counting them at all.
What happens with a repeating decimal like 0.333…?
It can only be approximated, never matched exactly. A fraction's decimal expansion terminates only when its reduced denominator has no prime factors besides 2 and 5, which is exactly what 1,000,000 is built from. Typing 0.333333 returns 333333⁄1,000,000 in lowest terms — a close neighbor of one-third, not one-third itself.
What is the most common mistake when reducing a fraction like this by hand?
Stopping after removing one shared factor instead of the greatest one. Dividing 750,000 and 1,000,000 by 2 gives 375,000⁄500,000, which looks simpler but still shares a factor of 125,000 — reduction isn't finished until the greatest common divisor, not just any common divisor, has been removed.
What happens when the scaled numerator and the GCD turn out to be the same number?
That happens whenever the decimal is a clean power-of-two fraction. Type 0.125 and Scaled numerator (× 1,000,000) reads 125,000 — and GCD used to reduce also reports 125,000, since that is the largest shared factor. Dividing each by itself and by the other gives Numerator 1 and Denominator 8, recovering 0.125 = 1⁄8 directly.